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Algebraic Geodesy and Geoinformatics, second edition

Joseph Awange
Organization: Curtin University of Technology
Department: Spatial Sciences, Division of Resource and Environmental
Erik Grafarend
Organization: Stuttgart University
Department: Geodesy and Geoinformatics
Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Piroska Zaletnyik
Organization: Budapest University of Technology and Economics
Department: Department of Geodesy and Surveying
Book information

Publisher: Springer (Berlin)
Copyright year: 2010
ISBN: 9783642121234
Medium: Hardcover
Includes: CD-ROM
Pages: 377
Out of print?: N
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Introduction | Algebraic Symbolic and Numeric Methods | Basics of Ring Theory | Basics of Polynomial Theory | Groebner Basis | Polynomial Resultants | Linear Homotpy | Solutions of Overdetermined Systems | Extended Newton-Raphson Method | Procrustes Solution | Applications to Geodesy and Geoinformatics | LPS-GNSS Orientations and Vertical Deflections | Cartesian to Ellipsoidal Mapping | Position by Ranging | Positioning by Resection Methods | Positing by Intersection Methods | GNSS Environmental Monitoring | Algebraic Diagnosis of Outliers | Datum transformation Problems | Appendix

The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems illustrated with Mathematica using computer algebra techniques of Ring, Polynomials, Groebner basis, Resultants including Dixon resultant, Gauss-Jacobi combinatorial and Procrustes algorithms as well as homotopy methods. These problems are traditionally solved by approximate methods. This book presents alternative algebraic techniques based on computer algebra tools. This new approach meets such modern challenges as resection by laser techniques, solution of orientation in Robotics, transformation and bundle block adjustment in Geoinformatics, densification of Engineering networks, analytical solution for GPS-meteorology and many other problems. For Mathematicians, the book provides some practical examples of application of abstract algebra and multidimensional scaling. The accompanying CD-ROM contains Mathematica notebooks with computational illustrations and application packages to solve for real life problems in geodesy and geoinformatics as resection, intersection, orientation problems.

*Mathematics > Algebra
*Mathematics > Geometry

Algebra, Polynomials, Groebner basis, Dixon resultant, Gauss-Jacobi, Procrustes algorithms, Homotopy methods, Laser, Robotics, Geoinformatics, Engineering